The soldiers, from 1st Battalion The Royal Gurkha Rifles, died after being targeted at a joint patrol base in the Nahr-e Saraj district of Helmand Province at about 2am local time. Their families are being informed.

One soldier is believed to have been shot dead while in his sleeping quarters, the other two hit with fire from a rocket-propelled grenade launcher whilst in the tower guarding the base.

After launching what Liam Fox, the Defence Secretary, called a "pre-meditated attack", the Afghan soldier fled and is now on the run.

Afghanistan's President Hamid Karzai sent a letter of condolence to the UK offering his apologies for the incident, which also left another four British troops wounded.

It is not the first time foreign troops have been killed by renegade Afghan security forces, raising concern among some in the West about the degree of Taliban infiltration in state security forces trained and funded by the Nato as part of its fight against the resurgent militants.

Last November a rogue Afghan policeman killed five British soldiers in a training base in southern Helmand province.

The latest attack raises further question about the Nato mission in Afganistan and the ability of Afghan troops to take responsibility for their country's security.

It comes the day after Anders Fogh Rasmussen, the Nato chief, warned that David Cameron’s signal of a five-year timetable for withdrawing British troops risks encouraging the Taliban to step up their attacks on Western forces.

Mr Rasmussen insisted that Western nations must keep troops in Afghanistan “as long as necessary” and not set clear timelines for withdrawal.

Amid a mounting British death toll, polls say most voters want an end to the nine-year-old war, and Mr Cameron and his allies have been talking up the prospect of a British withdrawal from Afghanistan.

Lieutenant Colonel James Carr-Smith, spokesman for Task Force Helmand, said: "It is with deep sorrow I must inform you that three soldiers from the 1st Battalion The Royal Gurkha Rifles Battle Group were killed this morning in southern Nahr-e Saraj, Helmand Province.

"We believe these were the actions of a lone individual who has betrayed his Isaf and Afghan comrades.

"His whereabouts are currently unknown but we are making strenuous efforts to find him."

Isaf commander General David Petraeus said: "I echo the condolences and sentiments offered by president Karzai and the other Afghan officials.

"This is a combined, joint mission - Afghan and alliance troopers fighting shoulder-to-shoulder against the Taliban and other extremists.

"We have sacrificed greatly together, and we must ensure that the trust between our forces remains solid in order to defeat our common enemies."

The incident has echoes of the shootings carried out by an Afghan policeman at a checkpoint in Nad-e-Ali in Helmand Province on November 3.